Optical Flow and Trajectory Estimation Methods
This brief focuses on two main problems in the domain of optical flow and trajectory estimation: (i) The problem of finding convex optimization methods to apply sparsity to optical flow; and (ii) The problem of how to extend sparsity to improve trajectori
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Joel Gibson Oge Marques
Optical Flow and Trajectory Estimation Methods 123
SpringerBriefs in Computer Science Series editors Stan Zdonik Shashi Shekhar Jonathan Katz Xindong Wu Lakhmi C. Jain David Padua Xuemin (Sherman) Shen Borko Furht V.S. Subrahmanian Martial Hebert Katsushi Ikeuchi Bruno Siciliano Sushil Jajodia Newton Lee
More information about this series at http://www.springer.com/series/10028
Joel Gibson Oge Marques •
Optical Flow and Trajectory Estimation Methods
123
Joel Gibson Blackmagic Design Colorado Springs, CO USA
Oge Marques Department of Computer and Electrical Engineering Florida Atlantic University Boca Raton, FL USA
ISSN 2191-5768 ISSN 2191-5776 (electronic) SpringerBriefs in Computer Science ISBN 978-3-319-44940-1 ISBN 978-3-319-44941-8 (eBook) DOI 10.1007/978-3-319-44941-8 Library of Congress Control Number: 2016948603 © The Author(s) 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
To Andrea —Joel Gibson To Ingrid —Oge Marques
Preface
Optical flow can be thought of as the projection of 3-D motion onto a 2-D image plane. We are generally given the 2-D projections of the objects at different points in time, i.e., the images, and asked to ascertain the motion between these projections. While points of a physical object, considered at different points in time, should indeed have some dense motion vector in 3-D space, the projection of these points onto a 2-D image sacrifices this one-to-one characteristic. Indeed, it is ordinary that the projection of a point on an object is hidden or occluded from view or moved outside of the domain of the image. This inverse process is akin to trying to deduce objects from shadows cast on the ground. Yet understanding the motion within a scene is the key to solving many problems. With
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